Nimr was one of four Shi`ites put to death on January 2 alongside 43 Sunnis. All were convicted of "terrorism".

"We understand the Saudi anger over the attack on their facilities in Iran," a senior US State Department official said before Kerry`s arrival.

"But we also understand that lessening tensions is an important objective not only for the United States but for the region".

Saudi Arabia and its Gulf neighbours perceive a lack of US engagement in the region, particularly in the face of what they see as Iran`s "interference" in Yemen, Syria, Lebanon and elsewhere.

Those feelings crystallised with a historic international deal which this month lifted crippling economic sanctions on Iran in return for a scaling back of its nuclear capabilities.

Kerry has long sought to reassure his Gulf allies about the overtures to Iran, and will continue those efforts in Riyadh.Tensions between Saudi Arabia and Iran, the foremost Sunni and Shi`ite powers, have caused concern around the globe. China, France and Pakistan have all sought a de-escalation.

Iran`s supreme leader Ayatollah Ali Khamenei on Wednesday said the embassy attack was wrong, and against Islam.

"That was, I think from our perspective, extremely noteworthy," the State Department official said.

"And hopefully, maybe that will open up the possibility that the situation will resolve and that the Saudis will find their way forward in reopening their embassy in Tehran."

On Tuesday Saudi Arabia issued a 58-point "fact sheet" which it said illustrates "Iran`s aggressive policies" over nearly four decades.

Saudi Arabia and Iran support opposite sides in the Syria and Yemen wars.

But the State Department official said "one of the things that we think is relatively positive" is that neither Iran nor Saudi wants the bilateral problems to affect issues like Syrian peace negotiations.

"We also, of course, think that it`s important that the Saudis and the Iranians be able to have some kind of modus vivendi, if you will," that would allow a return to political negotiations on Yemen.

A Saudi-led military coalition since March has been supporting local forces and the internationally recognised government against the Iran-backed Huthi Shiite rebels.

During his one-day stop, Kerry is to meet Riad Hijab, general coordinator of Syria`s largest opposition coalition, ahead of UN-brokered peace talks.

Kerry arrived from the World Economic Forum in Davos, Switzerland, where on Thursday he expressed confidence that those talks will go ahead on Monday in Geneva despite a dispute over who would represent the country`s opposition.

Hijab insists the delegation from his High Committee should be the only opposition representative.

The committee`s decision to name a member of the Saudi-backed Islamist Jaish al-Islam rebel group as its chief negotiator has drawn criticism from some of its own members as well as opposition figures excluded from the coalition.